Statistics for Management Chapter 8 Time Series and Forecasting - - PowerPoint PPT Presentation

Statistics for Management

Chapter 8 – Time Series and Forecasting

Prepared and Delivered by, Sithari Herath

Statistics for Management_Time Series and Forecasting 1

Scope

• Variations in Time Series
• Cyclical Variation
• Forecasting

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Variations in in Tim ime Series

Term “Time Series” is used to refer any group of statistical information accumulated at regular intervals.

Four kinds of change, variation involved in time series:

• Secular trend – Value of the variable tend to increase or decrease
• Cyclical fluctuation – Business cycle
• Seasonal variation – Trend gets repeated from year to year
• Irregular variation – Unpredictable variation

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Cyclic lical l Varia iatio ion

Cyclical variation is the component of a time series that tends to oscillate above and below the secular trend line for periods longer than 1 year. Example: Below table elaborates grain received by farmers, cooperative over 8 years.

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Year (x) Actual bushels (‘000) (y) Estimated bushels (‘000) (y) 2012 7.5 7.6 2013 7.8 7.8 2014 8.2 8.0 2015 8.2 8.2 2016 8.4 8.4 2017 8.5 8.6 2018 8.7 8.8 2019 9.1 9.0

Bushels ('000) Year

Cyclical fluctuations above the trend line Trend line graph (y) Graph of actual points Cyclical fluctuations below the trend line

Measures of f cycli lical variation

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Percent of trend =

𝑧 𝑧 ∗ 100

Relative cyclical residual=

𝑧 −𝑧 𝑧

∗ 100

Example 1:

(a) Graph percent of trend. (b) Interpret percent of trend and relative cyclical residual for year 2019.

Example 2:

A computer firm specializing in software engineering, has complied the following revenue records for the years 2013 to 2019. Year 2013 2014 2015 2016 2017 2018 2019 Revenue (lacks) 1.1 1.5 1.9 2.1 2.4 2.9 3.5 (a) Apply measures of cyclical variation for above data. (b) Plot the percent of trend line. (c) In which year does the largest fluctuation of trend occur, and is it the same for both methods?

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Seasonal variation

Besides secular trend and cyclical variation, a time series also includes seasonal variation. Seasonal variation is defined as repetitive and predictable movement around the trend line in one year or less. In order to detect seasonal variation time intervals must be measured in small units, such as days, weeks, months, or quarters. Why seasonal variation?

• Establish the pattern of past changes.
• Project past patterns into the future.
• Eliminates seasonal patterns effects from the time series.

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Sim imple moving average

Example: ABC company has identified following sales values for past few months of the business. Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220 Calculate forecasted sales revenue for September applying 3-months moving average.

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Weighted moving average

Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220 Calculate forecasted sales revenue for September applying 3-months weighted moving average. (Use the weights 0.5, 0.3 and 0.2)

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Month Sales revenue ($) January 209 February 240 March 220 April 201 May 210 June 211 July 215 August 220

Exponential Smoothing

Calculate forecasted sales revenue for September applying 3-months weighted moving average. (Use alpha 0.3)

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Example

Following data represents number of repeated customers that were visiting a particular shop for 8 quarters. Year Quarter Number of repetitive customers 2018 Q1 35 Q2 32 Q3 27 Q4 30 2019 Q1 24 Q2 28 Q3 29 Q4 33 a) Forecast the number of repetitive customers for 2020 first quarter applying simple 2 quarter moving average. b) Forecast the number of repetitive customers for 2020 first quarter applying weighted 2 quarter moving average. (Use 0.6 to the latest quarter) c) Forecast the number of repetitive customers for 2020 first quarter applying exponential

• smoothing. (alpha =0.2)

d) If the actual number of repetitive customers was 34 for first quarter in 2020, conclude the most accurate method for above mentioned forecasting.

ThankYou!

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Questions

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